Cowabbi,
All the suggestions I made were for running off inverter...as Paul says, the square wave supply is rich in harmonics; in otherwords, there's more than just a 60 cycle supply feeding your gramophone. 60 cycles is the fundamental frequency doing the work, but there's many multiples of this frequency which extend into the audio spectrum (and no doubt RF) which is why you can hear the buzzing. You need to incorporate filtering between the inverter and the 120VAC input of the amplifier which will round off the edges of the square wave. Earthing can also help if the interference is getting in by some other stray path.
When I posted my previous reply I forgot to ask if you had changed all the leaky capacitors, high resistors, and dried out electrolytics, but as you've mentioned the sine wave supply runs the amp ok then that's not the problem.
As the amplifier is only of moderate gain (one triode and one pentode) I don't think it would be too difficult to solve the problem.
By the way, does the inverter noise vary with the volume? If so, it indicates it's being picked up around the amplifier input.
As for the motor running hot on the transformer (ie. 50 cycle supply), maybe it is the lower frequency causing that, but would be a sign of a motor made with as few turns of wire (ie. cost cutting) as they could get away with. The other thing is the actual transformer...one of my stepdown transformers is actually 220 to 120V, so with 240-250V fed into it and a very light load on the secondary the voltage is rather high ~135v. I don't use it for lamps or things with valve heaters.
One other thing also with AC/DC gear, because of the way the valve heaters are supplied, the heater to cathode insulation can be fairly stressed depending where certain valves are in the heater chain, and if this starts to fail you'll get evidence of hum.
